Forming matches between competing interests involves balancing individual preferences, which can be challenging, particularly when only a finite number of choices are available. In general, matches formed without factoring in the preferences of each participant carry the potential to be unstable, that is, the participants might later revisit their matches to attempt new matches more compatible with their own preferences. A stable match eliminates the possibility that participants might later attempt to change their matches by ensuring that no two parties will both have an incentive to break their existing matches to form a new match. Stable matches are often formed for real world applications, such as to match graduating medical students to residency programs at hospitals or to assign students to schools and universities.
Frequently, a neutral third party is engaged to form stable matches to ensure fairness and impartiality. Each participant must reveal their preferences to the third party at the expense of complete privacy. This sharing of preferences implicates a significant level of trust in the third party to keep the preferences confidential, particularly when the stable matches are based on a participant's least preferred choices. At best, the use of a trusted third party is a compromise, as complete privacy can only be ensured by preventing the third party from learning more about each participants' preferences than could otherwise be inferred by an outsider from the resulting stable match.
Moreover, encrypting communications in-transit between the participants and the third party fails to lessen the trust that the participants must place in the third party. Encrypting the communications only protects participants' preferences from eavesdroppers and the third party must still be trusted to keep the preferences private, even if no one else is able to learn the preferences. As a result, encryption alone fails to guarantee complete privacy, where no other parties, not even the third party, know the participants' preferences.
The revelation of participants' preferences presents a potential for abuse, whether the preferences are obtained from the third party through artifice or legitimate means. For example, knowledge of other participants' preferences could enable a dishonest participant to game the matching by biasing their own preferences to influence the outcome. Furthermore, placing all of the trust in a single third party is inherently risky and violates the basic security tenet that trust should be shared among multiple parties. Distributing trust helps to minimize the influence that can be asserted by any individual participant due to, for example, inequities in interests or power.
The Gale-Shapley stable matching algorithm, such as described in D. Gale and H. Shapley, “College Admissions and the Stability of Marriage,” Am. Math. Monthly (1962), the disclosure of which is incorporated by reference, presents one particularly well-known solution to forming stable matches using a trusted third party, which is described in the context of one-to-one matchings of men and women in marriage engagements. Every man and woman first ranks their respective preferences of women and men, with no ties allowed. The two groups of participants are all initially “free,” that is, unmatched. Arbitrarily, men propose to women. As long as at least one man remains unmatched, men are iteratively matched to the woman that they most prefer and to whom they have not previously attempted an engagement. If the woman is available, the man and woman are matched and move to the group of matched couples. Otherwise, if the woman is already engaged, she will only break her engagement if she has ranked the new suitor higher than the man to whom she is currently engaged. Her current fiancé will be “dumped” and returned to the group of free, unengaged men and a new couple will be formed. Although guaranteed to result in a set of stable matchings, the Gale-Shapley algorithm generates residual information at the termination of the algorithm that includes the complete lists of preferences for both sides and the histories of matches made and broken.
Therefore, there is a need for providing stable matches without revealing any information, either interim or upon completion, other than the final matches formed. Preferably, such an approach would be divisible among multiple cooperating matchmaking parties to avoid an over concentration of trust.
There is a further need for forming stable matches through one or more third parties that ensures complete privacy to participants by preventing the third parties from learning more about the participants' preferences than could otherwise be inferred by an outsider from the stable match.